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Popular >

extreme f(x)=x(x-2)e^{-3x}

Solution

extreme points

f (x) = x (x - 2) e^{- 3 x}

Solution

Minimum (\frac{4 - 10}{3}, \frac{2 e ^{- 4 + 10} - 2 10 e ^{- 4 + 10}}{9}), Maximum (\frac{4 + 10}{3}, \frac{2 10 e ^{- 4 - 10} + 2 e ^{- 4 - 10}}{9})

Solution steps

f^{'} (x) = - e^{- 3 x} (3 x^{2} - 8 x + 2)

Find intervals:

Decreasing

: - \infty < x < \frac{- 10 + 4}{3},

Increasing

: \frac{- 10 + 4}{3} < x < \frac{10 + 4}{3},

Decreasing

: \frac{10 + 4}{3} < x < \infty

Plug

x = \frac{4 - 10}{3}

into

x (x - 2) e^{- 3 x} : \frac{2 e ^{- 4 + 10} - 2 10 e ^{- 4 + 10}}{9}

Minimum (\frac{4 - 10}{3}, \frac{2 e ^{- 4 + 10} - 2 10 e ^{- 4 + 10}}{9})

Plug

x = \frac{4 + 10}{3}

into

x (x - 2) e^{- 3 x} : \frac{2 10 e ^{- 4 - 10} + 2 e ^{- 4 - 10}}{9}

Maximum (\frac{4 + 10}{3}, \frac{2 10 e ^{- 4 - 10} + 2 e ^{- 4 - 10}}{9})

Minimum (\frac{4 - 10}{3}, \frac{2 e ^{- 4 + 10} - 2 10 e ^{- 4 + 10}}{9}), Maximum (\frac{4 + 10}{3}, \frac{2 10 e ^{- 4 - 10} + 2 e ^{- 4 - 10}}{9})

Popular Examples

extreme f(x,y)=x^3-4xy+y^2 extreme points

f (x, y) = x^{3} - 4 x y + y^{2}

extreme f(t)=-4t^2+208t+120 extreme points

f (t) = - 4 t^{2} + 208 t + 120

extreme f(x)=2x^3-2x^4 extreme points

f (x) = 2 x^{3} - 2 x^{4}

extreme f(x)=sqrt(x)((x^2)/5-4)extreme points

f (x) = x (\frac{x ^{2}}{5} - 4)

extreme-x^2-6x-4 extreme points

- x^{2} - 6 x - 4

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(x-2)e^{-3x} ?
The extreme f(x)=x(x-2)e^{-3x} is